Student Book links Specification links Links to prior learning Suggested teaching order

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1 Teaching plan Velocity and acceleration Student Book links Specification links Links to prior learning Suggested teaching order Learning objectives 12 Students should be able to: explain the distinction between scalar and vector quantities distinguish between speed and velocity and define acceleration calculate values using equations for velocity and acceleration. Key terms GCSE SI units for motion GCSE calculations of speed, velocity and acceleration Use of a stop clock to measure times 1. Review of SI units and prefixes for kinematic quantities 2. Review of simple speed, distance, time calculations 3. Distinguishing average and instantaneous speeds 4. Definition and examples of scalar and vector quantities including distance/displacement and speed/velocity 5. Definition of acceleration and calculations of acceleration 6. Acceleration as a vector Practical skills Scalar Vector Speed Displacement Maths links Velocity Average speed Instantaneous speed Acceleration Determine average speed using a metre rule and stop clock (Practical techniques 1, 2, 4). Determine average speed using light gates and datalogger (Practical techniques 1, 2, 4, 11). Suggested activity Practical 2: Determine the acceleration of a freely-falling object (Core practical 1, Practical techniques 1, 4, 2 or 11; CPAC 2a b, 2d, 4b). Digital learning ideas Recognise and make use of appropriate units in calculations (C.0.1). Recognise and use expressions in decimal and standard form (C.0.2). Use ratios, fractions and percentages (C.0.3). Use calculators to find and use power, exponential and logarithmic functions (C.0.5). Understand and use the symbols: =, <, <<, >>, >,,, (C.2.1). Calculate rate of change from a graph showing a linear relationship (C.3.5). Distinguish between instantaneous rate of change and average rate of change (C.3.7). Use light gates and data logging software to measure displacements, velocities and accelerations. Use video capture and analysis software (e.g. using freeware such as Tracker). Use high speed cameras (if available) to capture and analyse rapid motion. 1

2 Teaching plan Velocity and acceleration Apply the concepts underlying calculus (but without requiring the explicit use of derivatives or x integrals) by solving equations involving rates of change, e.g. x using a graphical t method or spreadsheet modelling (C.3.9). Pre-unit homework suggestions Students should practise speed, distance, time calculations. Set students a research task to find out about the SI units for motion. Students should practise prefixes and powers of ten such as milli-, micro-, nano-, kilo-, mega-. Suggested starter activities Equipment Teacher notes 1. Pose a question such as At what speed does a fingernail grow? or At what speed does a spacecraft travel to the Moon? Ask students to discuss and then justify their answers. Homework, practice and support: Mastering Mechanics Laws of motion, Scalars and vectors Homework, practice and support: Maths Arithmetic and numerical calculations Using standard form, Units This introduces the idea of speed as distance divided by time and will involve a discussion of appropriate units (including prefixes). Both examples are likely to lead to a discussion of instantaneous versus average speed. It can also be used to discuss scientific notation and uncertainties. 2. Ask students, in pairs, to measure the average speed of a squash ball dropped from a height of 2.0 m. Squash ball, stop clock, metre rulers (two per group) or tape measure Plenty to draw out in discussion: the need to repeat a measurement, the distinction between average and instantaneous speed, the concept of acceleration, uncertainties in measurements ( Which is most significant time or distance? ). 3. Discuss distance, speed, velocity and acceleration of athletes taking part in 100 m and 400 m events. Suggested main activities Equipment Teacher notes The 400 m event involves a total displacement of 0 m and therefore an average velocity of 0 ms 1. To run 100 m in 10 s requires a maximum velocity of greater than 10 ms Analysis of a multi-flash photograph Multi-flash photograph(s) Search for multi-flash photography online or create images in class. 2

3 Teaching plan Velocity and acceleration 2. Practice with calculations This should not be underestimated. The basic equations and mathematical techniques are simple but students need to become proficient with interpreting a range of different dynamic contexts. 3. Use of light gates and data logging equipment to measure velocities and to calculate accelerations Light gate(s) and datalogger, inclined planes and trolley Velocity can be measured at different positions along the ramp or for different angles. Acceleration can be measured directly but better still from the velocity at two different positions and the time taken to move between them. 4. Analysis of motion using a webcam and Tracker software (or, if available, a high speed camera) Video camera, moving object (fast moving if a high speed camera is available), suitable software package If it is not possible to capture your own video, you can find public domain video clips online. Suggested plenary activities Equipment Teacher notes 1. Video analysis of an athletics event, for example a 100 m final at a major athletics event Students will need to understand frame rates and have some way of connecting a scale with the images. Freeware such as Tracker is excellent but you will require a lesson to teach students how to use it. Clips can be found on YouTube. The race can be started and stopped to estimate velocities at different points and to estimate the initial acceleration of the sprinter. 2. Quick quiz on units, prefixes, equations and terminology Ask students to fill in a partially completed table. 3. Ask each student to write a multiple choice question and solution based on the unit (divide into themes if necessary). Collect, check and collate questions then set as a class test. Setters could be invited to review their own questions when the test is completed or returned. This could involve peer-to-peer marking. Homework suggestions Provide a list of moving things and ask students to estimate their speed and give an explanation of how they did this. The list could include: a cheetah; a 100 m sprinter; a racing car; a falling raindrop; a snail; growth rate of a tree, a strand of hair, a child or a fingernail. The important point is that they consider distance travelled and time taken and can justify their responses/units/notation. Students should practise calculations of average speed, velocity and speed (in situations where they need to be distinguished), and acceleration, for example Q1 3 from the Student Book. 3

4 Teaching plan Velocity and acceleration Wider reading Research the definitions of metre and second. Support ideas Practise simple calculations of speed, distance and time. Extension ideas Consider vector acceleration in circular motion: How can something have constant speed but be accelerating? Potential misconceptions The concept of a rate of change is challenging and will need reinforcement through a variety of examples. Confusion between velocity and acceleration may occur. The motion of a ball thrown vertically and caught can be used to consolidate and extend ideas about vectors and scalars. It can also be used to help the understanding of velocity and acceleration, for example: How can the ball be accelerating downwards whilst moving upwards?, How can the ball be accelerating when it is instantaneously at rest at the top of its motion?, How does the velocity and displacement change with time? Links to future learning Consideration of how displacement, velocity, and acceleration change with time links to the graphical representation of motion Vector addition and subtraction, and resolution of vectors along particular axes: If I travel 50 km NW how far north do I go? The idea of cause for acceleration, such as gravity for a projectile, as a link from acceleration to resultant force Differentiation for AS students Although the idea of acceleration when an object moves along a curved path reinforces the vector nature of acceleration, AS students will not study circular motion so this challenging idea could be omitted. Notes 4

5 Practical 2 Student sheet Determine the acceleration of a freely-falling object Practical 2: Determine the acceleration of a freely-falling object Objectives To measure the acceleration due to gravity g of an object falling freely and consider the following alternative methods: (a) object falling through a trap door (b) object falling through a light gate Safety Ensure that any apparatus that might topple over is secure. Be aware of falling objects. All the maths you need Use ratios, fractions and percentages (k here is the measurement students make). uncertainty Percentage uncertainty (%U) = mean value 100% Percentage difference (%D) = ( k g) g Find arithmetic means. The mean of a range of data = 100% sum of readings number of readings Translate information between graphical, numerical and algebraic forms. Plot two variables from experimental or other data. Understand that y = mx + c represents a linear relationship. Determine the slope and intercept of a linear graph. Equipment metre ruler or tape measure with millimetre resolution For (a): steel sphere electronic timer electromagnet to retain steel sphere trap door Procedure For (b): falling object, such as a 2 cm dowel, 10 cm long means to guide dowel through light gate light gate and datalogger 1. Drop the object from rest and record the time taken t for: (a) the sphere to fall to the trap door (b) the dowel to pass through the light gate. 2. Repeat the measurement for (a) and (b) twice more and work out the mean value. 3. Measure and record the height h fallen by the object. 4. Repeat the timing of the drop as you vary the height; you should take at least 6 readings. 5. Use half the range in your readings for t as the uncertainty in t. Calculate the percentage uncertainty in t. 6. For method (b) you should measure the length of the dowel. All users will need to review the risk assessment information and may need to adapt it to local circumstances. 1

6 Practical 2 Student sheet Determine the acceleration of a freely-falling object Analysis of results 1. Plot a graph of t 2 (y-axis) against h (x-axis) and work out the gradient m of the line of best fit. 2. Calculate a value for g where g = 2 m. 3. Use your value for the length of the dowel to calculate the mean speed v of the dowel as it passes through the light gate. 4. Plot a graph of v 2 against h and work out the gradient m of the line of best fit. 5. Calculate a value for g, where g = 2 m. 6. The percentage uncertainty (%U) in t 2 is twice that in t. Use this to draw on your plot s error bars in the y direction only. You can use a typical mid-range value for calculating uncertainties and need not work out a separate error bar for each value. Draw further lines of fit to calculate the %U in your value for g. 7. Calculate the percentage difference (%D) between your value and the accepted value of 9.81 ms 2 and comment on the accuracy of your method. Learning tips Ensure that points plotted on a graph take up more than half of the available space on both scales. You do not always need the origin on a graph. Keep scales simple, one big square as 5, 10 or 20 is ideal. One big square as 3 or 7 is very difficult to plot on and often leads to errors. Always consider whether or not the graph line should go through the origin. Straight lines should be drawn with aid of a ruler one long enough to cover the full length of the line. Since the object is falling at constant acceleration, use the appropriate SUVAT equation. 1 2 (a) s ut a t where u = 0, a = g, and s = h 2 t 2 = 2h g and comparison with y = mx + c shows that plotting t2 against h should be a straight line passing through the origin with gradient 2 g (b) v 2 = u 2 + 2as where u = 0, a = g, and s is h. v 2 = 2gh and comparison with y = mx + c shows that plotting v 2 against h should be a straight line passing through the origin with gradient 2g. Questions 1. Describe any advantage in using light gates in this experiment. 2. Discuss the effect of air resistance on your value for g. 3. Explain why the graph should be a straight line. Exam-style questions 1. An experiment to determine a value for the acceleration of freefall g is carried out by dropping a sphere through a measured height onto a trap door. It is found necessary to drop the object over a distance larger than about 30 cm. Explain why this technique is likely to produce more repeatable results. 2. An experiment to determine a value for the acceleration of freefall g is carried out by dropping a dowel through a measured height so that it passes through a light gate. Give two reasons why the repeatability of the readings is likely to reduce as the distance fallen gets longer. All users will need to review the risk assessment information and may need to adapt it to local circumstances. 2

7 Practical 2 Teacher sheet Determine the acceleration of a freely-falling object Practical 2: Determine the acceleration of a freely-falling object Objectives To measure the acceleration due to gravity g of an object falling freely and consider the following alternative methods: (a) object falling through a trap door (b) object falling through a light gate Safety Ensure security of any apparatus that might topple over. Be aware of falling objects. Procedure 1. Drop the object from rest and record the time taken t for: (a) the sphere to fall to the trap door (b) the dowel to pass through the light gate. 2. Repeat the measurement for (a) and (b) twice more and take the mean value. 3. Measure and record the height h fallen by the object. 4. Repeat the timing of the drop as you vary the height; you should take at least 6 readings. 5. Use half the range in your readings for t as the uncertainty in t. Calculate the percentage uncertainty in t. 6. For method (b) you should measure the length of the dowel. Answers to questions Specification links Core practical 1 Practical techniques 1, 4, 2 or 11 dependent on method CPAC 2a, 2b, 2d, 4b Notes on procedure It may be interesting to have two groups of students using the two methods separately to see if different results are produced. This would be a good experiment to practise handling the uncertainties, especially in the square of a quantity. Offering students a choice of methods will start their path towards mastery of practical physics, and use of investigative techniques (CPAC 2). 1. There should be less uncertainty in the measurement of time but this will be of interest particularly if the class have used both methods. 2. Students value for g will have been reduced by air resistance. They should use the %D in their remarks. 3. A straight line has a constant gradient. The line should be straight because the gradient depends only on g, which is constant. Answers to exam-style questions 1. A drop of more than 30 cm will mean that the time measured is longer, so the percentage uncertainties will be smaller making the result more repeatable. 2. The time to pass through the light gate gets shorter at greater lengths, so the percentage uncertainties will be higher. Assuming that air resistance will not vary appreciably, and hence the repeatability will not be affected, there is more chance of the dowel hitting the guide and slowing down. All users will need to review the risk assessment information and may need to adapt it to local circumstances. 1

8 Practical 2 Teacher sheet Determine the acceleration of a freely-falling object Sample data v/ms 1 h/m This data was obtained using a 100 mm object falling through a light gate. The datalogger calculated the speed. This gives a value for g of 9.48 ms 2. The graph does have an intercept All users will need to review the risk assessment information and may need to adapt it to local circumstances. 2

9 Practical 2 Technician sheet Determine the acceleration of a freely-falling object Practical 2: Determine the acceleration of a freely-falling object Objectives To measure the acceleration due to gravity g of an object falling freely and consider the following alternative methods: (a) object falling through a trap door (b) object falling through a light gate Equipment per student/group metre ruler or tape measure with millimetre resolution Notes on equipment (a) steel sphere (a) electronic timer (a) electromagnet to retain steel sphere (a) trap door 5 10 mm diameter Standard timer Connect the electromagnet to the timer so that switching off the current starts the timer. Connect the trap door so that the timer stops when the trap door opens. (b) falling object, such as a 2 cm dowel, 10 cm long (b) means to guide dowel through light gate Two pieces of curtain track, held a distance apart, or a length of 30 mm diameter acrylic tube would work well (b) light gate and datalogger Notes All users will need to review the risk assessment information and may need to adapt it to local circumstances. 1

10 Assessment 2.1 Motion 1 Which of the following is a vector? A kinetic energy B momentum C mass D speed Your answer (1) (Total for Question 1 = 1 mark) 2 A sports car accelerates from 10 ms 1 to 40 ms 1 in 5.0 s. Which line in the table below gives the correct values for distance travelled, average speed and acceleration during the 5.0 s? Distance/m Average speed/ms 1 Acceleration/ms 2 A B C D Your answer (1) (Total for Question 2 = 1 mark) 1

11 Assessment 2.1 Motion 3 A cable car at rest is suspended from a cable as shown below. The tension in the cable is T and the weight of the cable car is W. Which of the equations below is correct? A 2T = W B 2T sin (80 ) = W C 2T cos (80 ) = W D 2T + W = 0 Your answer (1) (Total for Question 3 = 1 mark) 2

12 Assessment 2.1 Motion 4 A uniform metre ruler can be balanced horizontally by placing a 100 g mass on the ruler 5.0 cm from one end and putting a pivot under the ruler at 30.0 cm from the same end as shown below. What is the mass of the metre ruler? A 100 g B 125 g C 400 g D There is not enough information to calculate the mass of the ruler. Your answer (1) (Total for Question 4 = 1 mark) 3

13 Assessment 2.1 Motion 5 The diagram below shows a velocity time graph for a vehicle of mass 2000 kg over a 35 s time period. (a) State the feature of the graph that represents the acceleration of the vehicle. (1) (b) State the feature of the graph that represents the displacement of the vehicle. (1) (c) (i) Calculate the acceleration during the first 10 s. (1) (ii) Calculate the total displacement of the vehicle during the 35 s. (ii) Calculate the braking force on the vehicle during the final 5 s. (Total for Question 5 = 7 marks) 4

14 Assessment 2.1 Motion 6 The diagram below shows a car towing a caravan at constant velocity along a straight horizontal road. The car and caravan each have a mass of 1200 kg and the total drag force on each vehicle is 1000 N. (a) State the magnitude of the forward force from the car and explain your answer. (b) State the magnitude of the tension in the tow link. Justify your answer. (c) Explain how the forces acting at the point where the tow link connects to the car illustrate Newton s third law of motion. (3) (d) The tow link suddenly breaks. Calculate the initial acceleration of the car. (Total for Question 6 = 9 marks) TOTAL FOR ASSESSMENT = 20 MARKS 5

15 EDEXCEL Physics Teacher Resource Pack Mark scheme 2.1 Motion Question number Answer Additional guidance Mark 1 B (1) (Total for Question 1 = 1 mark) Question number Answer Additional guidance Mark 2 C (1) (Total for Question 2 = 1 mark) Question number Answer Additional guidance Mark 3 C (1) (Total for Question 3 = 1 mark) Question number Answer Additional guidance Mark 4 B (1) (Total for Question 4 = 1 mark) 1

16 EDEXCEL Physics Teacher Resource Pack Mark scheme 2.1 Motion Question number Answer Additional guidance Mark 5(a) Gradient Accept slope. (1) 5(b) Area under the graph (1) 5(c)(i) 3.0 ms 2 Value and unit are required. (1) 5(c)(ii) 825 m Allow 1 mark for correct calculation of any section (150 m, 600 m, 75 m). 5(c)(iii) Deceleration = 6.0 ms 2 (1) Braking force = N (1) No unit marks (Total for Question 5 = 7 marks) Question number Answer Additional guidance Mark 6(a) 2000 N (1) 6(b) 1000 N (1) Constant velocity so there is no resultant force (1) Forward force on caravan must balance drag force (1000 N) for constant velocity (or for no resultant force on caravan) (1) 6(c) Force on the towing link from the car (1) is equal to the force on the car from the towing link (1) but acts in the opposite direction. (1) 6(d) Resultant force = 1000 N (1) a = F m = 0.83 ms 2 (1) Allow 1 mark for a correct statement of the third law. (3) (Total for Question 6 = 9 marks) 2